A211448 Number of (n+1)X(n+1) -7..7 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values

112, 842, 6350, 48066, 365098, 2782326, 21268302, 163031330, 1252859362, 9649453790, 74464405550, 575598981066, 4455555893866, 34529231972766, 267840329960454, 2079116664331442, 16147841707644970, 125461567656824486

Offset

1,1

Comments

Symmetry and 2X2 block sums zero implies that the diagonal x(i,i) are equal modulo 2 and x(i,j)=(x(i,i)+x(j,j))/2*(-1)^(i-j)

Links

R. H. Hardin, Table of n, a(n) for n = 1..136

Formula

Empirical: a(n) = 59*a(n-1) -1530*a(n-2) +22776*a(n-3) -212619*a(n-4) +1268503*a(n-5) -4641183*a(n-6) +8770309*a(n-7) -1702416*a(n-8) -18846228*a(n-9) +5437041*a(n-10) +28831259*a(n-11) +22145188*a(n-12) +8024466*a(n-13) +1548672*a(n-14) +152856*a(n-15) +6048*a(n-16)

Example

Some solutions for n=3
..1.-4.-1..0....1..0.-1.-2....3..0..5..1...-3.-1..2..2....7..0..6.-1
.-4..7.-2..3....0.-1..2..1....0.-3.-2.-4...-1..5.-6..2....0.-7..1.-6
.-1.-2.-3..2...-1..2.-3..0....5.-2..7.-1....2.-6..7.-3....6..1..5..0
..0..3..2.-1...-2..1..0..3....1.-4.-1.-5....2..2.-3.-1...-1.-6..0.-5

Crossrefs

Sequence in context: A264891 A203796 A203789 * A206318 A206311 A343372

Adjacent sequences: A211445 A211446 A211447 * A211449 A211450 A211451

Keyword

nonn

Author

R. H. Hardin Apr 11 2012

Status

approved